The Design of Stacked Linkages for Motion Generation

This paper introduces the concept of “stacked linkages” and develops an algorithm for the design of such linkages. A stacked linkage is defined as a linkage whose geometry is repeatedly stacked upon itself to produce a multiloop linkage where each loop in the linkage has a motion that is identical to every other loop within the linkage. The special geometry required by a stacked linkage produces a relatively simple design algorithm that can be applied to synthesize linkages of varying complexity. The synthesis process is based upon the ability to reduce the motion of a complex linkage to an equivalent motion for a four-bar linkage. The four-bar linkage can then be synthesized and stacked upon itself to give a complex linkage with the desired total motion. This method allows the designer to do a preliminary analysis of the linkage motion characteristics (such as transmission angles, circuits, and branching) by examining the motion characteristics of a simple four-bar chain. The algorithm presented in this paper is limited to the case of rigid body guidance for two design positions. Other cases may be possible with further development.